# sprfinal - Discrete Structures(COT 3100 Final Exam Spring...

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Discrete Structures (COT 3100) Final Exam Spring 2000 Section 2 4/25/00 Lecturer: Arup Guha TA: __________________ First Name : ________________ Last Name : ________________ (Note: On all questions that contain a blank line, please place your answer on that line clearly. If a short answer question doesn’t have a line for you to place your answer, please neatly write your answer directly below the question. Circle TRUE or FALSE for all true/false questions.)

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for leaving the question blank, and negative one point for an incorrect response. a) (p q) ( ¬ q ¬ p) TRUE b) 5 x 2200 y [x + y = 10] FALSE c) If the contrapositive of a statement is true, FALSE then the converse of statement is true as well. d) ¬ [ 2200 x p(x)] 5 x ¬ p(x) TRUE e) Let A, B and C be sets. If A B and A B = B C, then A = C. FALSE f) The total number of subsets of {2,4,5,6,9} is 25. FALSE g) If a | b and a | c, then gcd(b,c) a. TRUE h) If R is a bijection (A B), and S is a surjection (B C), then R ° S is an injection (A C). FALSE i) Let A and B be sets of strings such that A* B*, then A B. FALSE j) The number of bijective functions over a set A={1,2,3} is 6. TRUE k) A DFA must have more than one final state. FALSE l) A language containing a finite number of strings is a regular language. TRUE m) A DFA with n states that accepts at least one string MUST accept at least one string with a length less than or equal to n. TRUE n) a+ is NOT a valid regular expression. TRUE o) | λ | = 0. TRUE 2) (8 pts) Fill in the following Truth Table to evaluate the expression (p (q ¬ r)) (r ¬ q). p
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sprfinal - Discrete Structures(COT 3100 Final Exam Spring...

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